Analysis of stability and bifurcations of fixed points and periodic solutions of a lumped model of neocortex with two delays

A lumped model of neural activity in neocortex is studied to identify regions of multi-stability of both steady states and periodic solutions. Presence of both steady states and periodic solutions is considered to correspond with epileptogenesis. The model, which consists of two delay differential e...

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Bibliographic Details
Published inJournal of mathematical neuroscience Vol. 2; no. 1; p. 8
Main Authors Visser, Sid, Meijer, Hil GE, van Putten, Michel JAM, van Gils, Stephan A
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 25.04.2012
Springer Nature B.V
BioMed Central Ltd
Springer
Subjects
Applications of Mathematics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Neurosciences
Bifurcation Diagram
Periodic Solution
Hopf Bifurcation
Period Doubling Bifurcation
Stability Region
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Summary:A lumped model of neural activity in neocortex is studied to identify regions of multi-stability of both steady states and periodic solutions. Presence of both steady states and periodic solutions is considered to correspond with epileptogenesis. The model, which consists of two delay differential equations with two fixed time lags is mainly studied for its dependency on varying connection strength between populations. Equilibria are identified, and using linear stability analysis, all transitions are determined under which both trivial and non-trivial fixed points lose stability. Periodic solutions arising at some of these bifurcations are numerically studied with a two-parameter bifurcation analysis.
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ISSN:2190-8567
2190-8567
DOI:10.1186/2190-8567-2-8